Vice President Joe Biden laughs during a campaign rally at Lakewood High School on Nov. 12 in Lakewood, Ohio.

Matt Rourke/AP

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If the Electoral College fails to elect a vice president, the Senate votes on the two candidates for that office who received the most votes. Unlike in the House, each senator gets one vote, so the party that controls a majority in the Senate also decides the next vice president.

The Senate is currently controlled by Democrats, 51 to 47, with two independents voting with the majority caucus. Although Democrats are defending 23 of the 33 total seats up for election this cycle, Republicans have had setbacks in Missouri and Indiana, states they had been expected to win. The Cook Political Report projects that there is now only a "small possibility" that Republicans will win the majority in the Senate.

Thus, if senators were to vote along party lines, Vice President Biden could be reelected, this time to serve in a Republican administration, per the House decision. Moreover, if voters return a 50-50 Senate, as they did in the contested 2000 election, could it be Biden, in his capacity as president of the Senate, who winds up casting the tie-breaking vote that ensures his own reelection?

Congressional experts disagree on whether this tie-breaking option applies in the case of choosing a vice president. The 12th Amendment specifies that a majority of "the whole number of Senators" is necessary to choose the vice president. "The president of the Senate is not a senator," says Robert Dove, a former Senate parliamentarian. On a constitutional issue, the ruling of the Senate parliamentarian is likely to be taken especially seriously, but the chair is not required to follow it.

In short, the Senate typically operates by a combination of rules and precedent. In this case, there is no precedent.